Pat is knitting a scarf on average she can knit 2cm in 35minutes

Mathematics

1 answer:

wlad13 [49]3 years ago

7 0

Answer:

Step-by-step explanation:

2cm per 35 min

1 cm per 17.5 min

17.5 minutes per cm

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Based on the Fundamental Theorem of Algebra, how many complex roots does each of the following equations have? Write your answer

Galina-37 [17]

According to the fundamental theorem of algebra, every polynomial of degree n has n complex zeroes.

Part A:

Given

$x(x^2-4)(x^2+16)=0 \\ \\ \Rightarrow x(x^4+12x^2-64)=0 \\ \\ \Rightarrow x^5+12x^3-64x=0$

Thus, the given polynomial is of degree 5 and hence has 5 omplrex roots.

Part B:

Given

$(x^2+4)(x+5)^2 = 0 \\ \\ \Rightarrow(x^2+4)(x^2+10x+25)=0 \\ \\ \Rightarrow x^4+10x^3+25x^2+4x^2+40x+100=0 \\ \\ \Rightarrow x^4+10x^3+29x^2+40x+100=0$

Thus, the polynomial is of degree 4 and hence has 4 complex roots.

Part C:

Given

$x^6-4x^5-24x^2+10x-3=0$

Thus, the given polynomial is of degree 6 and hence has 6 complex roots.

Part D:

Given

$x^7+128=0$

Thus, the given polynomial is of degree 7 and hence has 7 complex roots.

Part E:

Given

$(x^3+9)(x^2-4)=0 \\ \\ \Rightarrow x^5-4x^3+9x^2-36=0$

Thus, the given polynomial is of degree 5 and hence has 5 complex roots.

4 0

3 years ago

PLZ ANSWER THANK YOU

NikAS [45]

Answer:

1, x/3, x^2/9, x^3/27, x^4/81

x^4 +3x^3+9x^2+27x+81

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Step-by-step explanation:

(x/3) ^i

i=0 (x/3)^0 = 1

i=1 (x/3)^1 = x/3